Effects of stochastic interest rates and volatility on contingent claims

Japanese Economic Review

Volumn 58, Issue 1, 2007, Pages 71-106

  Kunitomo, Naoto ^a   Kim, Yong Jin ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b HOSEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

INTEREST RATE; NUMERICAL METHOD; PRICE DYNAMICS; STOCHASTICITY;

EID: 33947587635     PISSN: 13524739     EISSN: 14685876     Source Type: Journal    
DOI: 10.1111/j.1468-5876.2007.00345.x     Document Type: Article

References (49)

1. Amin, K. I. and R. A. Jarrow (1992) "Pricing Options on Risky Assets in a stochastic interest rate economy", Mathematical Finance, Vol. 4, pp. 217-237.
2. Amin, K. I. and V. C. Ng (1993) "Option Valuation with Systematic Stochastic Volatility", Journal of Finance, Vol. 48, pp. 881-910.
3. Baily, W. and R. M. Stulz (1989) "The Pricing of Stock Index Options in a General Equilibrium Model", Journal of Financial and Quantitative Analysis, Vol. 24, pp. 1-12.
4. Bakshi, G. S. and Z. Chen (1997) "An Alternative Valuation Model for Contingent Claims", Journal of Financial Economics, Vol. 44, pp. 123-165.
5. Bakshi, G. S. and D. Madan (2000) "Spanning and Derivative Security Valuation", Journal of Financial Economics, Vol. 55, pp. 205-238.
6. Ball, C. A. and A. Roma (1994) "Stochastic Volatility Option Pricing", Journal of Financial and Quantitative Analysis, Vol. 29, pp. 589-607.
7. Black, F. and M. Scholes (1973) "The Pricing of Options and Corporate Liabilities", Journal of Political Economy, Vol. 81, pp. 637-654.
8. Cox, J., J. Ingersoll and S. Ross (1981) "The Relation between Forwards Prices and Futures Prices", Journal of Financial Economics, Vol. 9, pp. 321-346.
9. Cox, J., J. Ingersoll and S. Ross (1985a) "An Intertemporal General Equilibrium Model of Asset Prices", Econometrica, Vol. 53, pp. 363-384.
10. Cox, J., J. Ingersoll and S. Ross (1985b) "A Theory of the Term Structure of Interest Rates", Econometrica, Vol. 53, pp. 385-408.
11. Duffie, D. (1996) Dynamic Asset Pricing Theory, 2nd Edition, Princeton: Princeton University Press.
12. Duffie, D., J. Pan and K. Singleton (2000) "Transform Analysis and Asset Pricing for Affin Jump Diffusions", Econometrica, Vol. 68, pp. 1343-1376.
13. Fouque, J-P., G. Papanicolaou and K. R. Sircar (2001) Derivatives in Financial Markets with Stochastic Volatility, Cambridge: Cambridge University Press.
14. Heath, D., R. Jarrow and A. Morton (1992) "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claim Valuation", Econometrica, Vol. 60, pp. 77-105.
15. Heath, D., E. Platen and M. Schweizer (2001) "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets", Mathematical Finance, Vol. 11, pp. 385-413.
16. Helmer, M. L. and F. A. Longstaff (1991) "General Equilibrium Stock Index Futures Prices: Theory and Empirical Evidence", Journal of Financial and Quantitative Analysis, Vol. 26, pp. 287-308.
17. Heston, S. L. (1993) "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options", Review of Financial Studies, Vol. 6, pp. 327-343.
18. Hull, J. and A. White (1987) "The Pricing of Options on Assets with Stochastic Volatilities", Journal of Finance, Vol. 42, pp. 281-300.
19. Hull, J. and A. White (1988) "An Analysis of the Bias in Option Pricing Caused by a Stochastic Volatility", Advances in Futures and Options Research, Vol. 3, pp. 29-61.
20. Ikeda, N. and S. Watanabe (1989) Stochastic Differential Equations and Diffusion Processes, New York: North-Holland.
21. Johnson, H. and D. Shanno (1987) "Option Pricing when the Variance Is Changing", Journal of Financial and Quantitative Analysis, Vol. 22, pp. 143-151.
22. Karatzas, I. and S. Shreve (1998), Methods of Mathematical Finance, New York: Springer.
23. Kim, Y-J. (2002) "An Econometric Analysis of Japanese Derivatives Market", Unpublished Ph.D. Dissertation, Graduate School of Economics, University of Tokyo.
24. Kim, Y-J. and N. Kunitomo (1999) "Pricing Options under Stochastic Interest Rates: A New Approach", Asia-Pacific Financial Markets (Kluwer), Vol. 6, pp. 49-70.
25. Kunitomo, N. and A. Takahashi (1995) "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims", Discussion Paper No.95-F-19, Faculty of Economics, University of Tokyo. (Presented at the Japan-Russia Symposium on Probability and Mathematical Statistics, Tokyo.)
26. Kunitomo, N. and A. Takahashi (1998) "On Validity of the Asymptotic Expansion Approach in Contingent Claims Analysis", Discussion Paper No.98-F-6, Faculty of Economics, University of Tokyo.
27. Kunitomo, N. and A. Takahashi (2001) "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims", Mathematical Finance, Vol. 11, pp. 117-151.
28. Kunitomo, N. and A. Takahashi (2003a) "On Validity of the Asymptotic Expansion Approach in Contingent Claims Analysis", Annals of Applied Probability, Vol. 13, pp. 914-952.
29. Kunitomo, N. and A. Takahashi (2003b) A Foundation of Mathematical Finance: Applications of Malliavin Calculus and Asymptotic Expansion, Tokyo: Toyo-keizai-Shinposha. (In Japanese).
30. Kunitomo, N. and A. Takahashi (2004) "Applications of the Asymptotic Expansion Approach based on Malliavin-Watanabe Calculus in Financial Problems", in J. Akahori, S. Ogawa and S. Watanabe (eds), Stochastic Processes and Applications to Mathematical Finance, Hackensack, NJ: World Scientific, pp. 195-232.
31. Merton, R. C. (1973) "Theory of Rational Option Pricing", Bell Journal of Economics and Management Science, Vol. 4, pp. 141-183.
32. Nagai, H. (1999) Stochastic Differential Equation, Tokyo: Kyoritsu. (In Japanese).
33. Rabinoviteh, R. (1989) "Pricing Stock and Bond Options when the Default-free Rate is Stochastic", Journal of Financial and Qualitative Analysis, Vol. 24, pp. 447-457.
34. Romano, M. and N. Touzi (1997) "Contingent Claims and Market Completeness in a Stochastically Volatility Model", Mathematical Finance, Vol. 7, pp. 399-412.
35. Scott, L. O. (1987) "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application", Journal of Financial and Quantitative Analysis, Vol. 22, pp. 419-438.
36. Scott, L. O. (1997) "Pricing Stock Options in a Jump-Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods", Mathematical Finance, Vol. 7, pp. 413-426.
37. Shigekawa, H. (1998) Stochastic Analysis, Tokyo: Iwanami-Shoten. (In Japanese).
38. Sircar, R. and G. Papanicolaou (1999) "Stochastic Volatility, Smile and Asymptotics", Applied Mathematical Finance, Vol. 6, pp. 107-145.
39. Sørensen, M. and Yoshida, N. (2000) "Random Limit Expansion for Small Diffusion Processes", mimeo.
40. Stein, E. M. and J. C. Stein (1991) "Stock Price Distributions with Stochastic Volatility: An Analytic Approach", Review of Financial Studies, Vol. 4, pp. 727-752.
41. Takahashi, A. (1995) "Essays on the Valuation Problems of Contingent Claims", Unpublished Ph.D. Dissertation, Business Administration, University of California, Berkeley.
42. Takahashi, A. (1999) "An Asymptotic Expansion Approach to Pricing Contingent Claims", Asia-Pacific Financial Markets (Kluwer), Vol. 6, pp. 115-151.
43. Takahashi, A. and N. Yoshida (2004) "An Asymptotic Expansion Scheme for the Optimal Portfolio Investment", Statistical Inference for Stochastic Processes, Vol. 7, pp. 153-188.
44. Takahashi, A. and N. Yoshida (2005) "Monte Carlo Simulation with Asymptotic Method", Journal of Japan Statistical Society, Vol. 35, pp. 171-203.
45. Turnbull, S. M. and F. Milne (1991) "A Simple Approach to Interest-Rate Option Pricing", Review of Financial Studies, Vol. 4, pp. 87-120.
46. Watanabe, S. (1987) "Analysis of Wiener Functionals (Malliavin Calculus) and its Applications to Heat Kernels", Annals of Probability, Vol. 15, pp. 1-49.
47. Wiggins, J. B. (1987) "Option Values under Stochastic Volatility: Theory and Empirical Estimates", Journal of Financial Economics, Vol. 19, pp. 351-372.
48. Yoshida, N. (1992) "Asymptotic Expansion for Statistics Related to Small Diffusions", Journal of Japan Statistical Society, Vol. 22, pp. 139-159.
49. Yoshida, N. (2003) "Conditional Expansions and Their Applicatons", Stochastic Processes and Their Applications, Vol. 107, pp. 53-81.